In this paper, the laser tomographic reconstruction process is described. Several methods (virtual DM, virtual layer projection) are studied, under the constraint of a single matrix vector multiplication. The pseudo-synthetic interaction matrix model and the LTAO reconstructor design are analysed. Moreover, the reconstruction parameter space is explored, in particular the regularization terms.
Furthermore, we present here the strategy to define the modal control basis and split the reconstruction between the Low Order (LO) loop and the High Order (HO) loop. Finally, closed loop performance obtained with a 3D turbulence generator will be analysed with respect to the most relevant system parameters to be tuned.